"Examples of mock modular forms"의 두 판 사이의 차이
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| 9번째 줄: | 9번째 줄: | ||
<h5>mock theta conjectures</h5> | <h5>mock theta conjectures</h5> | ||
| + | * <cite class="" id="CITEREFWatson1936" style="font-style: normal;">Watson, G. N. (1936), "The Final Problem : An Account of the Mock Theta Functions", <em>J. London Math. Soc.</em>'''11''': 55–80, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1112%2Fjlms%2Fs1-11.1.55 10.1112/jlms/s1-11.1.55]</cite> | ||
| + | * <cite class="" id="CITEREFWatson1937" style="font-style: normal;">Watson, G. N. (1937), "The Mock Theta Functions (2)", <em>Proc. London Math. Soc.</em>'''s2-42''': 274–304, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1112%2Fplms%2Fs2-42.1.274 10.1112/plms/s2-42.1.274]</cite> | ||
* [http://dx.doi.org/10.1016/0001-8708%2889%2990070-4 Ramanujan's “Lost” Notebook VI: The mock theta conjectures]<br> | * [http://dx.doi.org/10.1016/0001-8708%2889%2990070-4 Ramanujan's “Lost” Notebook VI: The mock theta conjectures]<br> | ||
** George E. Andrews and F. G. Garvan | ** George E. Andrews and F. G. Garvan | ||
| + | * | ||
* <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "A proof of the mock theta conjectures", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 639–660, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394279 10.1007/BF01394279], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | * <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "A proof of the mock theta conjectures", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 639–660, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394279 10.1007/BF01394279], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | ||
* <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "On the seventh order mock theta functions", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 661–677, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394280 10.1007/BF01394280], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | * <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "On the seventh order mock theta functions", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 661–677, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394280 10.1007/BF01394280], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | ||
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* <cite class="" id="CITEREFChoi1999" style="font-style: normal;">Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''136''' (3): 497–569, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2Fs002220050318 10.1007/s002220050318], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1695205 1695205], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | * <cite class="" id="CITEREFChoi1999" style="font-style: normal;">Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", <em>[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''136''' (3): 497–569, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2Fs002220050318 10.1007/s002220050318], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1695205 1695205], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | ||
| 26번째 줄: | 27번째 줄: | ||
* <cite class="" id="CITEREFAndrews1988" style="font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em>Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite> | * <cite class="" id="CITEREFAndrews1988" style="font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em>Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite> | ||
| + | * [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions]<br> | ||
| + | ** Basil Gordon and Richard J. Mcintosh | ||
2009년 5월 18일 (월) 14:28 판
Examples
classify which examples are of which use
mock theta conjectures
- Watson, G. N. (1936), "The Final Problem : An Account of the Mock Theta Functions", J. London Math. Soc.11: 55–80, doi:10.1112/jlms/s1-11.1.55
- Watson, G. N. (1937), "The Mock Theta Functions (2)", Proc. London Math. Soc.s2-42: 274–304, doi:10.1112/plms/s2-42.1.274
- Ramanujan's “Lost” Notebook VI: The mock theta conjectures
- George E. Andrews and F. G. Garvan
- Hickerson, Dean (1988), "A proof of the mock theta conjectures", Inventiones Mathematicae94 (3): 639–660, doi:10.1007/BF01394279, MR969247, ISSN0020-9910
- Hickerson, Dean (1988), "On the seventh order mock theta functions", Inventiones Mathematicae94 (3): 661–677, doi:10.1007/BF01394280, MR969247, ISSN0020-9910
- Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", Inventiones Mathematicae136 (3): 497–569, doi:10.1007/s002220050318, MR1695205, ISSN0020-9910
- Choi, Youn-Seo (2000), "Tenth order mock theta functions in Ramanujan's lost notebook. II", Advances in Mathematics156 (2): 180–285, doi:10.1006/aima.2000.1948, MR1808245, ISSN0001-8708
- Choi, Youn-Seo (2002), "Tenth order mock theta functions in Ramanujan's lost notebook. IV", Transactions of the American Mathematical Society354 (2): 705–733, doi:10.1090/S0002-9947-01-02861-6, MR1862564, ISSN0002-9947, http://www.jstor.org/stable/2693766
- Choi, Youn-Seo (2007), "Tenth order mock theta functions in Ramanujan's lost notebook. III", Proceedings of the London Mathematical Society. Third Series94 (1): 26–52, doi:10.1112/plms/pdl006, MR2293464, ISSN0024-6115
order 5
- Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", Ramanujan revisited (Urbana-Champaign, Ill., 1987),
- Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions
- Basil Gordon and Richard J. Mcintosh
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표준적인 도서 및 추천도서
- 찾아볼 수학책
- http://gigapedia.info/1/Polyogarithms
- http://gigapedia.info/1/ramanujan
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
참고할만한 자료
- http://www.zentralblatt-math.org/zmath/en/
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Mock_modular_form
- http://viswiki.com/en/
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=
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